N - mixture models by species

modelling N by site to get relative abundance

abundance by site will be used as a cov on predator occupancy

7 models evaluated, dot, jdt + jdtSQ, lure + jdt + jdtSQ


Species:      rodent



Metadata Summary:

N_sites N_counts N_detections rep_period iterations burnin thin
127 3291 708 7 days 120000 20000 10



Detections by Year:

Yr 2016 2017 2018 2019 2020
sites 19 31 19 32 26
detections 172 202 113 108 113
N.dot.model 21 39 31 49 65



WAIC

Models by WAIC:
model description WAIC N.total.est
fm7 counts 69.99641 127
fm6 lure + jdt + jdtSq 2960.26811 204
fm5 jdt + jdtSq 2994.33509 247
fm4 lure + jdt 3002.02919 202
fm2 jdt 3048.63247 251
fm1 dot 3072.02958 205
fm3 lure 3126.63791 246



Model summaries:



model: fm1
dot



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
p[1] NA 6541 0.367 0.367 0.32 0.42 0 1.001
p[2] NA 1909 0.214 0.225 0.15 0.27 0 1.001
p[3] NA 3497 0.100 0.097 0.07 0.13 0 1.001
p[4] NA 2290 0.072 0.068 0.04 0.10 0 1.001
p[5] NA 1548 0.062 0.056 0.04 0.09 0 1.001
lambda[1] NA 10000 1.144 1.043 0.74 1.54 0 1.001
lambda[2] NA 2708 1.416 1.281 0.88 1.93 0 1.001
lambda[3] NA 4988 1.782 1.632 1.10 2.45 0 1.001
lambda[4] NA 2648 1.785 1.64 1.02 2.46 0 1.001
lambda[5] NA 1244 2.693 2.193 1.44 3.80 0 1.001
N[36] NA 4888 1.893 2.002 1.00 3.00 0 1.0005
N[17] NA 10000 1.000 err 1.00 1.00 err err
N[125] NA 3814 3.542 2.994 1.00 6.00 0 1.0008
N[78] NA 6396 0.733 0 0.00 2.00 1 err
N[60] NA 6198 2.286 2.003 1.00 3.00 0 1.0008

p[1]

p[2]

p[3]

p[4]

p[5]

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[36]

N[17]

N[125]

N[78]

N[60]







model: fm2
jdt



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha jdt 9116 0.445 0.447 0.37 0.52 0 1.001
alpha0 NA 1752 -2.232 -2.211 -2.42 -2.04 0 1.001
lambda[1] NA 3478 3.258 3.137 2.31 4.18 0 1.001
lambda[2] NA 3122 2.781 2.617 1.97 3.52 0 1.001
lambda[3] NA 4982 1.826 1.77 1.20 2.40 0 1.001
lambda[4] NA 5980 1.221 1.185 0.84 1.59 0 1.001
lambda[5] NA 5323 1.824 1.75 1.26 2.35 0 1.001
N[114] NA 9535 1.165 err 1.00 2.00 err err
N[117] NA 6212 1.779 2.002 1.00 3.00 0 1.0005
N[43] NA 4710 4.550 4.002 3.00 6.00 0 1.001
N[102] NA 5700 2.735 2.999 2.00 4.00 0 1.001
N[96] NA 8366 1.128 err 1.00 2.00 err err

alpha

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[114]

N[117]

N[43]

N[102]

N[96]

alpha relationship







model: fm3
lure



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha lure 8110 -0.114 -0.116 -0.20 -0.03 0.13005 0.9816
alpha0 NA 1959 -2.135 -2.127 -2.32 -1.96 0 1.001
lambda[1] NA 3726 3.473 3.373 2.47 4.48 0 1.001
lambda[2] NA 2707 2.621 2.422 1.89 3.30 0 1.001
lambda[3] NA 5915 1.634 1.555 1.09 2.19 0 1.001
lambda[4] NA 5407 1.240 1.184 0.87 1.62 0 1.001
lambda[5] NA 5753 1.709 1.667 1.19 2.21 0 1.001
N[39] NA 7096 2.930 3 2.00 4.00 0 1.0009
N[88] NA 9655 0.031 err 0.00 0.00 err err
N[94] NA 6901 1.371 1 1.00 2.00 0 1.0001
N[66] NA 7025 1.940 err 1.00 3.00 err err
N[68] NA 7053 2.088 err 1.00 3.00 err err

alpha

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[39]

N[88]

N[94]

N[66]

N[68]

alpha relationship







model: fm4
lure + jdt



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha[1] lureDays 4712 -0.461 -0.461 -0.58 -0.35 0 1.001
alpha[2] julianDt 5282 0.634 0.631 0.54 0.73 0 1.001
alpha0 NA 1776 -2.084 -2.083 -2.28 -1.89 0 1.001
lambda[1] NA 3590 1.968 1.889 1.26 2.64 0 1.001
lambda[2] NA 3694 1.956 1.872 1.37 2.57 0 1.001
lambda[3] NA 5391 1.463 1.419 0.92 1.96 0 1.001
lambda[4] NA 6228 1.084 1.025 0.72 1.41 0 1.001
lambda[5] NA 5040 2.143 2.067 1.51 2.76 0 1.001
N[38] NA 7684 1.974 1 1.00 3.00 0 1.0005
N[31] NA 5540 1.881 err 1.00 2.00 err err
N[4] NA 5665 2.135 err 1.00 3.00 err err
N[14] NA 9118 1.034 err 1.00 1.00 err err
N[29] NA 8738 3.006 2.997 2.00 5.00 0 1.0009

alpha[1]

alpha[2]

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[38]

N[31]

N[4]

N[14]

N[29]







model: fm5
jdt + jdtSq



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha[1] julianDt 2625 -0.086 -0.089 -0.22 0.05 0.62267 0.8412
alpha[2] julianDtSq 2553 0.557 0.572 0.43 0.68 0 1.001
alpha0 NA 2071 -2.232 -2.219 -2.41 -2.05 0 1.001
lambda[1] NA 3910 3.800 3.681 2.73 4.82 0 1.001
lambda[2] NA 3434 2.379 2.287 1.72 3.04 0 1.001
lambda[3] NA 5764 1.917 1.9 1.28 2.51 0 1.001
lambda[4] NA 7056 1.129 1.094 0.78 1.47 0 1.001
lambda[5] NA 5562 1.839 1.797 1.29 2.35 0 1.001
N[87] NA 7820 2.588 3 2.00 4.00 0 1.0009
N[116] NA 8382 2.729 3.002 2.00 5.00 0 1.0009
N[109] NA 6562 1.832 2.002 1.00 3.00 0 1.0005
N[25] NA 6636 2.597 3 2.00 4.00 0 1.0009
N[52] NA 9611 0.062 err 0.00 0.00 err err

alpha[1]

alpha[2]

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[87]

N[116]

N[109]

N[25]

N[52]

julian date relationship







model: fm6
lure + jdt + jdtSq



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha[1] lureDays 5139 -0.401 -0.397 -0.50 -0.29 0.00000 1.0010
alpha[2] julianDt 2385 0.141 0.141 -0.01 0.29 0.33039 0.9320
alpha[3] julianDtSq 2552 0.508 0.501 0.38 0.63 0.00000 1.0010
alpha0 NA 2024 -2.131 -2.123 -2.30 -1.94 0.00000 1.0010
lambda[1] NA 3830 2.423 2.277 1.64 3.21 0.00000 1.0010
lambda[2] NA 4019 1.817 1.735 1.28 2.37 0.00000 1.0010
lambda[3] NA 6151 1.608 1.491 1.05 2.14 0.00000 1.0010
lambda[4] NA 8066 1.043 1.029 0.71 1.36 0.00000 1.0010
lambda[5] NA 4780 2.126 2.050 1.49 2.75 0.00000 1.0010
N[123] NA 8919 3.054 2.997 2.00 5.00 0.00000 1.0009
N[116] NA 7914 2.960 2.001 2.00 5.00 0.00000 1.0009
N[112] NA 8646 1.449 1.000 1.00 2.00 0.00000 1.0001
N[2] NA 6569 2.264 2.002 1.00 3.00 0.00000 1.0008
N[27] NA 6538 2.242 2.002 2.00 3.00 0.00000 1.0009

alpha[1]

alpha[2]

alpha[3]

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[123]

N[116]

N[112]

N[2]

N[27]







model: fm7
counts



summary table

param covariate iters_ef mean mode hdi_89pct_lower hdi_89pct_upper bayes_P pct.density
alpha counts 7143 34.612 34.62 32.35 36.91 0 1.001
alpha0 NA 7133 2.571 2.534 2.18 2.95 0 1.001
lambda[1] NA 10458 0.993 0.924 0.62 1.36 0 1.001
lambda[2] NA 10000 0.998 0.965 0.70 1.31 0 1.001
lambda[3] NA 10000 0.980 0.958 0.59 1.34 0 1.001
lambda[4] NA 10000 0.981 0.946 0.67 1.29 0 1.001
lambda[5] NA 10000 0.998 0.952 0.68 1.31 0 1.001
N[9] NA 0 1.000 err 1.00 1.00 err err
N[34] NA 0 1.000 err 1.00 1.00 err err
N[28] NA 0 1.000 err 1.00 1.00 err err
N[89] NA 10000 1.051 err 1.00 1.00 err err
N[82] NA 10000 1.005 err 1.00 1.00 err err

alpha

alpha0

lambda[1]

lambda[2]

lambda[3]

lambda[4]

lambda[5]

N[9]

## Warning in cor(X, use = "pairwise.complete.obs"): the standard deviation is zero
## Warning: Removed 50 rows containing missing values (geom_bar).

N[34]

## Warning in cor(X, use = "pairwise.complete.obs"): the standard deviation is zero
## Warning: Removed 50 rows containing missing values (geom_bar).

N[28]

## Warning in cor(X, use = "pairwise.complete.obs"): the standard deviation is zero
## Warning: Removed 50 rows containing missing values (geom_bar).

N[89]

N[82]

alpha relationship

## Warning: Removed 3 row(s) containing missing values (geom_path).